Is the concept of "spacetime" just a way for us to make peace with what we observe, or does it provide insight into what's "actually" going on? Is the concept of "spacetime" just a way for us to make peace with what we observe, or does it provide insight into what's actually going on?
 A: Your question has an answer which applies to physics in its entirety.
Whenever we try to explain something in Physics; we come up with a model/hypothesis to explain a particular phenomenon. Then the model/hypothesis is extensively tested for inconsistencies and when people are satisfied that the model/hypothesis is correct, these become Laws.
Now, we never know what is "actually" happening. But present laws are the best ways to explain these phenomenon. If and when a better alternative comes along, we replace the existing law with the new one.
So although it might seem a bit creepy, we never know what is actually going on. But we always make peace with the best possible explanation.
So, the proper question to pose from a physics point of view is not "What is actually happening?" but "What is the best explanation for this phenomenon?"
A: 
Is the concept of "spacetime" just a way for us to make peace with what we observe, or does it provide insight into what's actually going on?

I consider myself a relativist. I think relativity is one of the best-tested theories we've got, and a very important theory too. As such I think spacetime provides insight into what's actually going on. 
But there's a problem. When you read the original material by Einstein Minkowski and others, you come to appreciate that there's a gulf between relativity "as it was written" and relativity "as it is taught". Spacetime offers a prime example of this. It's actually a mathematical space. You draw worldlines in it to represent motion through space over time, and use a version of Pythagoras's theorem for spacetime intervals. It  works. Only then you bump into people who've been taught some weird ersatz cargo-cult version of relativity, people who talk about motion through spacetime, people who confuse space with spacetime. You try to show them some material where Einstein talks about space as distinct from spacetime, and you try to explain that Minkowski died too young to qualify what he said in Space and Time:
"Henceforth, space for itself, and time for itself shall completely reduce to a mere shadow, and only some sort of union of the two shall preserve independence".
But it's very difficult to get them to read about the original material and compare it to what they've been taught and with the hard scientific evidence. They come out with things like "your pencil falls down because spacetime is curved" even though Einstein never said that, and it's just not true. This wrong concept of spacetime doesn't  provide insight into what's going on. It might be a way for some to make peace with what we observe, but that stands four-square in the way of scientific progress. And in this Einstein's GR centenary year, some of us are damned if we're going to sit on our hands and do nothing about it.    
